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This paper focuses on nonlinear parameter identification of an equivalent circuit model for lithium-ion batteries (LiBs). A Thevenin's model is considered, which consists of a voltage source based on the battery's open-circuit voltage (OCV), an Ohmic resistor and two RC circuits connected in series. The objective is to identify all the parameters in the voltage source and circuits at once from the current-voltage data collected from a battery under constant-current discharging. Based on the voltage response, identifiability of the parameters is analyzed using the sensitivity analysis, and it is verified that the parameters are locally identifiable. An optimization problem based on nonlinear least squares is formulated to address identification, to which parameter bounds are imposed to limit the search space. The identification is then achieved by a trust region method. An evaluation based on experimental data illustrates the effectiveness of the proposed results. Differing from the existing work, this approach does not require an explicit relationship between the OCV and the battery's state- of-charge (SoC). Its application hence requires much less effort. Furthermore, the success in parameter identification can potentially contribute to parameter-analysis-based aging prognostics of LiBs.